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A158565 A modulo two based Pascal's triangle using powers of two for even and powers of three for odd: t(n,m)=If[Mod[Binomial[n, m], 2] == 0 && m <= Floor[n/2], 2^m, If[Mod[Binomial[n, m], 2] == 0 && m > Floor[n/2], 2^(n - m), If[Mod[Binomial[n, m], 2] == 1 && m <= Floor[n/2], 3^m, If[Mod[Binomial[n, m], 2] == 1 && m > Floor[n/2], 3^(n - m), 0]]]]. 0
1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 2, 4, 2, 1, 1, 3, 4, 4, 3, 1, 1, 2, 9, 8, 9, 2, 1, 1, 3, 9, 27, 27, 9, 3, 1, 1, 2, 4, 8, 16, 8, 4, 2, 1, 1, 3, 4, 8, 16, 16, 8, 4, 3, 1, 1, 2, 9, 8, 16, 32, 16, 8, 9, 2, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, 4, 8, 10, 16, 32, 80, 46, 64, 104,...}.

LINKS

Table of n, a(n) for n=0..65.

FORMULA

t(n,m)=If[Mod[Binomial[n, m], 2] == 0 && m <= Floor[n/2], 2^m,

If[Mod[Binomial[n, m], 2] == 0 && m > Floor[n/2], 2^(n - m),

If[Mod[Binomial[n, m], 2] == 1 && m <= Floor[n/2], 3^m,

If[Mod[Binomial[n, m], 2] == 1 && m > Floor[n/2], 3^(n - m), 0]]]].

EXAMPLE

{1},

{1, 1},

{1, 2, 1},

{1, 3, 3, 1},

{1, 2, 4, 2, 1},

{1, 3, 4, 4, 3, 1},

{1, 2, 9, 8, 9, 2, 1},

{1, 3, 9, 27, 27, 9, 3, 1},

{1, 2, 4, 8, 16, 8, 4, 2, 1},

{1, 3, 4, 8, 16, 16, 8, 4, 3, 1},

{1, 2, 9, 8, 16, 32, 16, 8, 9, 2, 1}

MATHEMATICA

Table[Table[If[Mod[Binomial[n, m], 2] == 0 && m <= Floor[n/2], 2^m,

If[Mod[Binomial[n, m], 2] == 0 && m > Floor[n/2], 2^(n - m),

If[Mod[Binomial[n, m], 2] == 1 && m <= Floor[n/2], 3^m,

If[Mod[Binomial[n, m], 2] == 1 && m > Floor[n/2], 3^(n - m),

0]]]], {m, 0, n}], {n, 0, 10}];

Flatten[%]

CROSSREFS

Sequence in context: A093557 A098802 A048804 * A132422 A065133 A343033

Adjacent sequences:  A158562 A158563 A158564 * A158566 A158567 A158568

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Mar 21 2009

STATUS

approved

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Last modified May 14 16:23 EDT 2021. Contains 343884 sequences. (Running on oeis4.)